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Acta Physica Sinica

Improvement on reflectivity of tunable photonic band gap with spontaneous generated coherence

Liu Shuan Yang, Gao Zhong-Xing, Bing Xue, Zhang Yong-Gang, Cai Yong-Mao

Published Jan 1, 2018• 0 citations
Publisher

Abstract

The photonic band gap is a spectral range which cannot propagate in a periodic optical nanostructure, that is, the structure itself has a “forbidden band”. It has been successfully applied to the filters, amplifiers, mixers, etc. As is well known, dynamically tunable photonic band gaps in cold atomic lattices are of great importance in various research fields. However, the photonic band gaps of a traditional photonic crystal are non-tunable because the periodic structure is determined once the photonic crystal is grown. On the other hand, a majority of previous researches focused on improving the reflectivity of photonic band gap, which can only keep approaching to 1. Due to the action of the vacuum of the radiation field, near-degenerate lower level has an additional coherence term, the spontaneously generated coherence term. In this paper, we consider a three-level ∧-type atomic system driven by a strong coherent field, a weak coherent field and an incoherent pump, in which the two ground states are of hyperfine structure. The one-dimensional photonic band gaps are formed by cold atoms trapped in a one-dimensional-ordered optical lattice and this system may create two photonic band gaps (PBGs). The trapped cold atoms have a Gaussian density distribution in each period as determined by the optical potential depth and the average atomic temperature. We investigate in detail how the reflectivities of the two PBGs are influenced by the coherent effect of spontaneously generated coherence. Then, we find that the reflectivities of the two band gaps can be significantly improved by the spontaneously generated coherence. The reflectivities of such two band gaps can be dynamically manipulated by varying the intensity of incoherent driving field and the relative phase between the probe field and the coupling field, which cannot be realized in a conventional ∧-type atomic system. Besides, by adjusting the parameters appropriately, the reflectivities of these two band gaps can be higher than 1, which is because probe field gain stems from the spontaneously generated coherence. In the future, photonic transport properties can be investigated in the three-dimensional atomic lattices and this work is meaningful for the optical routing, photodiode and transistor.

DOI
10.7498/aps.67.20181374

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The photonic band gap is a spectral range which cannot propagate in a periodic optical nanostructure, that is, the structure itself has a “forbidden band”. It has been successfully applied to the filters, amplifiers, mixers, etc. As is well known, dynamically tunable photonic band gaps in cold atomic lattices are of great importance in various research fields. However, the photonic band gaps of a traditional photonic crystal are non-tunable because the periodic structure is determined once the photonic crystal is grown. On the other hand, a majority of previous researches focused on improving the reflectivity of photonic band gap, which can only keep approaching to 1. Due to the action of the vacuum of the radiation field, near-degenerate lower level has an additional coherence term, the spontaneously generated coherence term. In this paper, we consider a three-level ∧-type atomic system driven by a strong coherent field, a weak coherent field and an incoherent pump, in which the two ground states are of hyperfine structure. The one-dimensional photonic band gaps are formed by cold atoms trapped in a one-dimensional-ordered optical lattice and this system may create two photonic band gaps (PBGs). The trapped cold atoms have a Gaussian density distribution in each period as determined by the optical potential depth and the average atomic temperature. We investigate in detail how the reflectivities of the two PBGs are influenced by the coherent effect of spontaneously generated coherence. Then, we find that the reflectivities of the two band gaps can be significantly improved by the spontaneously generated coherence. The reflectivities of such two band gaps can be dynamically manipulated by varying the intensity of incoherent driving field and the relative phase between the probe field and the coupling field, which cannot be realized in a conventional ∧-type atomic system. Besides, by adjusting the parameters appropriately, the reflectivities of these two band gaps can be higher than 1, which is because probe field gain stems from the spontaneously generated coherence. In the future, photonic transport properties can be investigated in the three-dimensional atomic lattices and this work is meaningful for the optical routing, photodiode and transistor.
We study both the steady and the dynamic optical response of cold atoms trapped in an optical lattice and driven to the three-level $\mathrm{\ensuremath{\Lambda}}$ configuration. These atoms are found to exhibit gain without population inversion when an incoherent pump is applied to activate spontaneously generated coherence. Gain-assisted double photonic band gaps characterized by reflectivities over 100% then grow up near the probe resonance due to the periodic distribution of the atomic density. These band gaps along with the neighboring allowed bands of transmissivities over 100% can be tuned by modulating the control field in amplitude, frequency, and, especially, phase. Consequently it is viable to realize a reflector, an amplifier, or a splitter when a weak incident light pulse is totally reflected in the photonic band gaps, totally transmitted in the allowed bands, or equally reflected and transmitted in the intersecting regions. Our results have potential applications in all-optical networks with respect to fabricating dynamically switchable devices for manipulating photon flows at low-light levels.
We study a cold atomic sample coherently driven into the five-level triple-$\ensuremath{\Lambda}$ configuration for attaining a dynamically controlled triple photonic band-gap structure. Our numerical calculations show that three photonic band gaps with homogeneous reflectivities up to 9292%92 can be induced on demand around the probe resonance by a standing-wave driving field in the presence of spontaneously generated coherence. All these photonic band gaps are severely malformed with probe reflectivities declining rapidly to very low values when spontaneously generated coherence is gradually weakened. The triple photonic band-gap structure can also be attained in a five-level chain-$\ensuremath{\Lambda}$ system of cold atoms in the absence of spontaneously generated coherence, which however requires two additional traveling-wave fields to couple relevant levels.
Using the technique of electromagnetically induced transparency, three photonic bandgaps can be established and manipulated at any time due to the refraction modulated periodically by the one-dimensional optical lattice in a tripod atomic system which is trapped in a one-dimensional optical lattice with a Gaussian density distribution. Using the density-matrix equations to describe the interaction between laser and atoms and the transfer-matrix equation to describe the scattering of light waves in periodic media, we can obtain the steady reflection and transmission spectra. It can be found that the position and width as well as the reflectivity of the photonic band-gap could be tuned by changing the detunings and intensities of the coupling fields and the geometric Bragg detuning.
We study an ensemble of cold atoms driven to the four-level double-$\ensuremath{\Lambda}$ configuration and trapped in the one-dimensional optical lattices for achieving dynamically controlled photonic band gaps (PBGs) via the balanced four-wave mixing interaction. Numerical results show that a pair of PBGs characterized by high platforms of probe reflectivities and reduced density of photonic states are established, simultaneously, on both probe transitions in one symmetric driving scheme. Such two-color PBGs can be easily manipulated in position and width by modulating, e.g., the balanced Rabi frequencies of two coupling fields and the Gaussian widths of atomic density distributions, to change the equal probe detunings fulfilling both Bragg conditions. Each two-color PBG as predicted in the coherent atomic lattices may be explored to attain robust light entanglement, even for single-probe photons, via an efficient frequency conversion during the nonlinearly correlated reflection.
An optical lattice loaded with cold atoms can exhibit a tunable photonic band gap for a weak probe field under the conditions of electromagnetically induced transparency. This system possesses a number of advantageous properties, including reduced relaxation of Raman coherence and the associated probe absorption, and simultaneous enhancement of the index modulation and the resulting reflectivity of the medium. This flexible system has the potential to serve as a test bed for various designs of linear and nonlinear photonic band gap materials at very low light level and can be employed to realize deterministic entanglement between weak quantum fields.
Summary form only given. Unlike semiconductors which facilitate the coherent propagation of electrons, photonic band gap (PBG) materials execute their novel functions through the coherent localization of photons. When a PBG material is doped with impurity atoms which have an electronic transition that lies within the gap, spontaneous emission of light from the atom is inhibited. Inside the gap, the photon forms a bound state to the atom. Outside the gap, radiative dynamics in the colored vacuum is highly nonMarkovian. I discuss the influence of these memory effects on laser action. When spontaneous emission is absent, the next order radiative effect (resonance dipole-dipole interaction between atoms) must be incorporated, leading to anomalous nonlinear optical effects which occur at a much lower threshold than in ordinary vacuum. I describe the collective switching of two-level atoms near a photonic band edge, by external laser field, from a passive stare to one exhibiting population inversion. This effect is forbidden in ordinary vacuum. Finally, I discuss the prospects for a phase sensitive, single (3-level) atom quantum memory device, onto which information may be written by an external laser pulse. By scattering polarized photons (flying qubit) this system may execute certain quantum logic operations.